Problem: Solve for $x$ and $y$ using elimination. ${-x-4y = -19}$ ${x-3y = -9}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-7y = -28$ $\dfrac{-7y}{{-7}} = \dfrac{-28}{{-7}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x-4y = -19}\thinspace$ to find $x$ ${-x - 4}{(4)}{= -19}$ $-x-16 = -19$ $-x-16{+16} = -19{+16}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {x-3y = -9}\thinspace$ and get the same answer for $x$ : ${x - 3}{(4)}{= -9}$ ${x = 3}$